Optimal averaged pade-type approximants

Pade-type approximants are rational functions that approximate a given formal power series. Spalevic'; [Math. Comp., 76 (2007), pp. 1483-1492] proposed optimal averaged Gauss quadrature rules, that have higher degree of precision than the corresponding averaged Gauss rules, with the same number of nodes. This paper defines Pade-type approximants associated with optimal averaged Gauss rules. Numerical examples illustrate their perfomance.